Answer:
(16)^-1 or (4)^-2
Step-by-step explanation:
(-1/4)^2, we can convert this to (1/16), which is (16)^-1 or (4)^-2.
Answer:
[tex]\frac{1}{16}[/tex]
Step-by-step explanation:
[tex]-\frac{1}{4} ^{2}[/tex]
[tex]\frac{-1^{2} }{4^{2} }[/tex]
[tex]=\frac{1}{16}[/tex]
FACTORISE THIS EXPRESSTION AS FULLY AS POSSIBLE 4x2+x3
Step-by-step explanation:
4x2 + x3
Rearrange
x3 + 4x2
x2 (x + 4)
F(x)=3x2 +12x +5 what is the discriminant
Answer:
84
Step-by-step explanation:
This is in the form
ax^2 + bx +c
3x^2 +12x +5
a =3 b = 12 c =5
The discriminant is
b^2 - 4ac
12^2 - 4 * 3 *5
144 - 60
84
Complete the square to make a perfect square trinomial. Write the result as a binomial square. q2−23q
Answer:
[tex]\left(q-\dfrac{23}{2}\right)^2[/tex]
Step-by-step explanation:
Given the expression: [tex]q^2-23q[/tex]
To complete the square, we follow these steps:
Step 1: Identify the coefficient of q
Coefficient of q=-23
Step 2: Divide the coefficient of q by 2
[tex]=-\dfrac{23}{2}[/tex]
Step 3: Square your result from step 2 and add it to the equation
This gives us: [tex]q^2-23q+\left(-\dfrac{23}{2}\right)^2[/tex]
We have now completed the square.
Step 4: Write the result as a binomial square.
To write it as a binomial square, pick the variable and add the term in the bracket.
Therefore:
[tex]q^2-23q+\left(-\dfrac{23}{2}\right)^2=\left(q-\dfrac{23}{2}\right)^2[/tex]
The perfect square form of the given expression will be [tex](q-\dfrac{23}{2})^2[/tex].
The given expression is [tex]q^2-23q[/tex].
It is required to write the given expression as a perfect square polynomial or trinomial.
We will use the identity [tex](a+b)^2=a^2+2ab+b^2[/tex].
So, the first term from the given expression will be [tex]a=q[/tex].
To find the second term b, divide the 2nd term of the given expression by 2,
[tex]b=\dfrac{-23}{2}[/tex]
So, the given expression can be written in the perfect square form as,
[tex]a^2+2ab+b^2=q^2-23q+(\dfrac{-23}{2})^2\\=(q-\dfrac{23}{2})(q-\dfrac{23}{2})\\=(q-\dfrac{23}{2})^2[/tex]
Therefore, the perfect square form of the given expression will be [tex](q-\dfrac{23}{2})^2[/tex].
For more details, refer to the link:
https://brainly.com/question/18875994
Which of the following is an advantage to using equations?
Answer:
The correct option is
(A). When given two names for the same quantity, you can use algebra to solve the equations.
Step-by-step explanation:
I had thesame quiz, lucky you...next time put the options :)
What’s the correct answer for this question?
Answer:
x = 40
Step-by-step explanation:
Given 2 secants to a circle from an external point, then
The product of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant, that is
8(8 + x) = 12(12 + 20) ← distribute parenthesis on both sides
64 + 8x = 12 × 32 = 384 ( subtract 64 from both sides )
8x = 320 ( divide both sides by 8 )
x = 40
Researchers conduct a study of obesity in children. They measure body mass index (BMI), which is a measure of weight relative to height. High BMI is an indication of obesity. Data from a study published in the Journal of the American Dietetic Association shows a fairly strong positive linear association between mother’s BMI and daughter’s BMI (r = 0.506). This means that obese mothers tend to have obese daughters. A. Identify explanatory, response, and potential lurking variables in this study. B. Can we conclude from this study that maternal obesity causes obesity in daughters?
Answer:
Step-by-step explanation:
a. The explanatory variables in this case is the mothers BMI on which the child's BMI is determined.
The response variable is the child's BMI which is also the outcome variable that exists if a child has an obese parent.
Other lurking variables may include the diets and exercise plan of either of these two variables.
b. No, this study cannot be used to conclude that maternal obesity causes obesity in daughters if the lurking variables are not dealt with.
Let x stand for the number of minutes spent waiting in line for a rollercoaster at an amusement park. 81 people are sampled at a time. The sample mean is 18 minutes and the sample standard deviation is 0.5 minutes. What is the standard deviation of the population?
Answer:
The standard deviation of the population is 4.5 minutes.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation of the population [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
In this question:
[tex]s = 0.5, n = 81[/tex]
So
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.5 = \frac{\sigma}{\sqrt{81}}[/tex]
[tex]\sigma = 9*0.5 = 4.5[/tex]
The standard deviation of the population is 4.5 minutes.
The total number of pupils in 6 classes is 192.
Find the average number of pupils in a class.
Somebody help please, I'm stuck with this question..
Answer:
32 pupils in a class
Step-by-step explanation:
You are going to divide 192 by 6 to figure out the average amount per class.
What is the value of x?
Answer:
The answer is B.
Step-by-step explanation:
Given that the total angle in a triangle is 180°. So in order to find x, you have to subatract 95° and 57° from 180°
[tex]x + 95 + 57 = 180[/tex]
[tex]x = 180 - 95 - 57[/tex]
[tex]x = 28[/tex]
Help asapa!! 30 poinst!!!
Answer:
The answer is option B
Step-by-step explanation:
I cant exactly explain it cus i dont remember but i know i got it right lol
but here goes
after she proves that AD is congruent to the other sides, all she has left to prove is ∠A≅∠B and AB≅BC.
'Tis how you get thine answer
(╯°□°）╯
Answer:
Option 1
Step-by-step explanation:
ABCD is a parallelogram, Julie wants to prove that ABCD is also a square.
Remember that a parallelogram has opposite sides equal.
So,
AB ≅ CD
AD ≅ BC
The 4 triangles are congruent. The bases of the triangles are vertically opposite to each other and are congruent. We can use the definition of a parallelogram to prove AB ≅ BC.
The outside temperature at 6:00 was 75º F. The temperature dropped 0.8ºF for the next 4 hours.What was the outside temperature after 4 hours?
Answer:
71.8° F
Step-by-step explanation:
Given 75° and 4 times 0.8° drop = 3.2°, so the temperature is 75° - 3.2°
= 71.8° F
Determine the equation of the inverse of y=2^3x-1
Answer:
f^-1(y) =[ In(x-2) + 1] /3
Step-by-step explanation:
The inverse of this expression is to find x
Now taking In of both sides we have
y=2^3x-1
In y = In2^3x-1
In y = (3x- 1)In 2
(Iny / In2) + 1= 3x
x =[ (Iny / In2) + 1] /3
Therefore the inverse of y is
f^-1(y) =[ (Inx / In2) + 1] /3
f^-1(y) =[ In(x-2) + 1] /3
The equation of the inverse of the provided equation, which is equal to the reverse of the original equation, is y=(ln(x-2)+1)/3.
What is the inverse of an equation?The inverse of an equation is the reverse of the original equation. The equation and the inverse of it has symmetry in each other.
To find the inverse of equation, we have to interchange the variable of equation to each other.
The given equation is,
[tex]y=2^{3x-1}[/tex]
Taking log both side of the equation,
[tex]\ln y = \ln 2^{3x-1}[/tex]
Use the log of power and simplify the equation further, as,
[tex]\ln y = \ln 2^{3x-1}\\\ln y = (3x-1)\ln 2\\\dfrac{\ln y}{\ln 2} = (3x-1)\\\ln (y-2)= (3x-1)\\\ln (y-2)+1= 3x\\x=\dfrac{\ln (y-2)+1}{3}[/tex]
Interchange the place of x and y,
[tex]y=\dfrac{\ln (x-2)+1}{3}[/tex]
This is the required inverse equation.
Thus, the equation of the inverse of the provided equation which is equal to the reverse of the original equation, is y=(ln(x-2)+1)/3.
Learn more about the inverse of an equation here;
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Tienes un triángulo equilátero con lados de 10cm, lo divides en dos partes de manera horizontal tal que el área de ambos figuras resultantes es igual, ¿cuánto vale la distancia del lado x?
Answer:
x = 10/√2 ≈ 7.07
Step-by-step explanation:
Comenzaremos por dividir el triángulo en dos partes y definir H, como en la figura adjunta.
Aplicando el teorema de Tales, sabemos que:
[tex]\dfrac{l/2}{H}=\dfrac{x/2}{h}\\\\\\\dfrac{l}{H}=\dfrac{x}{h}[/tex]
También sabemos que, dado que el tirángulo menor es la mitad que el triángulo mayor, la relación entre áreas es:
[tex]\dfrac{A}{A_x}=\dfrac{lH/2}{xh/2}=\dfrac{lH}{xh}=2[/tex]
Dado que formamos dos triángulos rectángulos, podemos despejar el valor de H como:
[tex](l/2)^2+H^2=l^2\\\\H^2=l^2-(l/2)^2=10^2-5^2=100-25=75\\\\H^2=\sqrt{75}[/tex]
Podemos entonces despejar x de la siguiente manera:
[tex]h=\dfrac{H}{l}\cdot x=\dfrac{lH}{2x}\\\\\\2x^2\dfrac{H}{l}=lH\\\\\\2x^2=l^2\\\\\\x=\dfrac{l}{\sqrt{2}}=\dfrac{10}{\sqrt{2}}\approx7.07[/tex]
Keep getting this wrong please help!!!
Answer:
85 + 35=120
Step-by-step explanation:
85 + 35= 120
85 - 35= 50
the difference is fifty
The composite figure is made up of a rectangular prism and a___a0___.a1
Answer:
The composite figure is made up of a rectangular prism and square pyramid
Step-by-step explanation:
The figure on top is square pyramid since the base is a square and the 4 sides are triangles. The bottom is a rectangular prism since the figure is made up of side rectangular faces
Answer:
square pyramid
also the figure has 896 cm2
Función inversa f(x) = 7/x -9
Answer:
F-1(x)=7/(x+9)
Step-by-step explanation:
Change F(x) to y so y=7/x -9
Swap variables x=7/y -9
Solve x+9=7/y
7/(x+9)=y
Then change y to F inverse
F-1(x)=7/(x+9)
Thats ur inverse!!!
Answer:
(x+9)/7
Step-by-step explanation:
Let f(x) = y;
y =7/x - 9
y + 9 = 7x
x = (y + 9)/7
Substitute x for y and X = f^{-1}(x)
f^{-1}(x) =(x+9)/7 this is the inverse of f(x)
It's in the pic plz help
Answer:
It is 4 because length PO is also 4 and TR is across from it.
Step-by-step explanation:
7) ¿De cuántas maneras pueden sentarse diez personas alrededor de una mesa circular?
Answer: Around a circular table, ten people can be seated 362880 ways.
Explanation:We establish the conditions of the exercise:
Yes, all elements fit. 10 people have to sit.Being a circular arrangement we must eliminate the circular repetitionsItems are not repeated. A person cannot be repeated.It is a Combination so we use the formula:
[tex]\boldsymbol{\sf{_{n}C_{r}=\cfrac{n!}{n\cdot (n-r)!} }}[/tex]
[tex]\boldsymbol{\sf{n=10\; \; \; \; \; r=10}}[/tex]
We substitute and solve:
[tex]\boldsymbol{\sf{_{10}C_{10}=\cfrac{10!}{10\cdot (10-10)!}=9!=9\cdot8\cdot7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1=362880}}[/tex]
Health issues are a concern of managers, especially as they evaluate the cost of medical insurance. A recent study of 150 executives at Elvers Industries, a large insurance and financial firm located in the Southwest, reported the number of pounds by which the executives were overweight. a. Compute the mean and the standard deviation.
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
Health issues are a concern of managers, especially as they evaluate the cost of medical insurance. A recent survey of 150 executives at Elvers Industries, a large insurance and financial firm located in the Southwest, reported the number of pounds by which the executives were overweight. Compute the mean and the standard deviation.
Pounds Overweight Frequency
0 up to 6 14
6 up to 12 42
12 up to 18 58
18 up to 24. 28
24 up to 30. 8
Solution:
This is grouped data. We would determine the midpoint or class mark, x of each class by taking their averages.
The table would become
Class. x f fx
0 up to 6 (0+6)/2 = 3 14 42
6 up to 12 (6+12)/2 = 9 42 378
12 up to 18 (12+18)/2 = 15 58 870
18 up to 24 (18+24)/2= 21 28 588
24 up to 30 (24+30)/2 = 27 8 216
Summation f = 14 + 42 + 58 + 28 + 8 = 150
Summation fx = 42 + 378 + 870 + 588 + 216 = 2094
Mean = Summation fx/Summation f
Mean, m = 2094/150 = 13.96
Standard deviation = √summation of f(x - m)²)/(n - 1)
We would create another column on the table
f x x - m f(x - m)²
14 3 - 10.96 1681.7024
42 9 - 4.96 1033.2672
58 15 1.04 62.7328
28 21 7.04 1387.7248
8 27 12.04 1159.6928
Total = 5325.12
Standard deviation = √5325.12/150 - 1)
Standard deviation = 5.98
Suppose that each customer asks to sample a food item with probability 1/4, independently of all other customers. The service time for a customer who samples a food item is an exponential random variable with parameter 1/5. i. What is the expected number of minutes until you reach the front of the line
Answer:
An approximately 2 minutes is expected to reach the front of the line
Step-by-step explanation:
Expected value of minutes =
(1/4)^(1/5) + (1 - 1/4)^(1/5)
= (1/4)^0.2 + (3/4)^0.2
= 0.7579 + 0.9441
= 1.702.
≈ 2 minutes
Determine whether the integral is convergent or divergent. 1 59 1 − x2 dx 0 convergent divergent Correct: Your answer is correct. If it is convergent, evaluate it. (If the quantity diverges, enter DIVERGES
Complete Question
The complete question is shown on the first uploaded image
Answer:
it is convergent and the solution is [tex]= \frac{33 \pi }{2}[/tex]
Step-by-step explanation:
From the question we are given
[tex]\int\limits^1_0 {\frac{33}{\sqrt{1-x^2} } } \, dx[/tex]
When integrated
[tex]= 33 sin^{-1} x \left | \ 1} \atop {0}} \right.[/tex]
[tex]= 33[ \frac{\pi }{2} - 0][/tex]
[tex]= \frac{33 \pi }{2}[/tex]
This implies that the integral converges
Use the DISTRIBUTIVE PROPERTY to simplify the expression. 4(3r - 8)
Answer:
12r-32
Step-by-step explanation:
Distribute the 4 between the different numbers.
3r * 4 = 12r and 8 * 4 = 32
So...you end up with 12r-32
Hi! I hope you're enjoying your day!
Let's recall that the Distributive Property states that
a(b+c)=ab+ac
Where
a, b, and c can be either constants (numbers like 4) or variables (letters like d)
Simplify:
4(3r-8)
4 times 3r is equal to 12r
12r- (4*8)
[tex]\boxed{\boxed{\bold{12r-32}}}[/tex]
Hope everything is clear.
If you have any questions, please comment.
#LearningIsFun
If LM = 41 – 2x and NP = 7x + 5, find LM.
What is the value of (3-5)4(2) – 16+ 2?
-40
-16
24
56
Answer:
-30
Step-by-step explanation:
(3-5)4(2) – 16+ 2= -2*8-14= -16-14= -30
A _ _ _ _ _ of a circle is a segment that begins and ends on the circle; a segment whose endpoints are on the circle. It does not have to pass through the center.
Answer:
Chord
Step-by-step explanation:
I believe the word you are looking for is a chord.
A book store is having a sale. The book Bart wants was originally priced at $14.99. The book is now $10.04. By what percentage was the price reduced?
Answer:
33.0220147 % reduction
Step-by-step explanation:
Take the original price and subtract the new price
14.99-10.04 = 4.95
Divide by the original price
4.95/14.99 =.330220147
Change to percent form
33.0220147 %
What is the value of x in the equation 3x - y = 18, when y= 27?
O 5
O 7
O45
O 63
Answer:
Step-by-step explanation:3x-y=18
y=27
Therefore 3x-(27)=18
3x=18+27..Nb when the 27 is now being added instead of subtracted.
3x=45
3x/3=45/3 Nb the 3 is now being divided instead of being multiplied.
Therefore X=15
The following ple chart shows the number of students in a certain school. There
are 2000 students in the school. Answer questions 21, 22 and 23 from the pie
chart.
Grade 1
30%
Grade 3
20%
Grade 4
15%
21. The number of students in grade 1 is
22. The number of students in grade 3 is
23. The number of students in grade 4 is
Answer:
G1 : 0.3(2000) = 600
G2: 0.2(2000) = 400
G3: 0.15(2000) = 300
G4: 2000/15=150
What is the volume of a cylinder with base radius 2 and height 5?
Answer:
20 pi (sign)
Step-by-step explanation:
khan answer trust me bro
Evaluate 3|-5| -2|-2|
Answer:
11
Step-by-step explanation:
absolute value is always a positive number so
3|-5| -2|-2| =
3 * 5 -2*2
follow PEMDAS
15 -4 = 11
